The Dinner and Dialogue Club has planned a series of small meetings. Each meeting would consist of two or three members enjoying friendly conversation with each other while eating food from different places all over the world. Each member is scheduled to meet exactly four times. No pair of members will meet twice, but some pairs might not meet at all.

The first thing the club did was schedule and arrange the meetings so that each member knew whom to meet and when. When it came to choosing restaurants, someone suggested that each member eat at two restaurants with eastern food, and two with western food (each restaurant is either one or the other). They liked the idea, but to their dismay, the idea was not possible without rearranging at least some of the meetings.

What possible meeting schedule might cause this to happen? How many members are there in this club, at the least?

There is a minimum of three people to attend 4 meetings each and eat two eastern and two western meals.
A=member 1
B=member 2
C=member 3
meeting one=A and C attend and eat Eastern
meeting two=A and B attend and eat Western
meeting three=B and C attend and eat Western
meeting four=A and C attend and eat Western
meeting five=A and B attend and eat Eastern
meeting six=B and C attend and eat Eastern

With that schedule all three members of the club would attend four meetings each and each eat two meals of Eastern and two meals of Western.

Posted by Jeramie on 2005-11-04 21:14:09